Optical Engineering 46͑9͒, 093604 ͑September 2007͒

Evaluation of brilliance, fire, and scintillation in round brilliant gemstones

Jose Sasian, FELLOW SPIE Abstract. We discuss several illumination effects in gemstones and University of Arizona present maps to evaluate them. The matrices and tilt views of these College of Optical Sciences maps permit one to find the stones that perform best in terms of illumi- 1630 East University Boulevard nation properties. By using the concepts of the main cutter’s line, and the Tucson, Arizona 85721 anti-cutter’s line, the problem of finding the best stones is reduced by E-mail: [email protected] one dimension in the cutter’s space. For the first time it is clearly shown why the Tolkowsky cut, and other cuts adjacent to it along the main cutter’s line, is one of the best round brilliant cuts. The maps we intro- Jason Quick duce are a valuable educational tool, provide a basis for gemstone grad- Jacob Sheffield ing, and are useful in the jewelry industry to assess gemstone American Gem Society Laboratories performance. © 2007 Society of Photo-Optical Instrumentation Engineers. 8917 West Sahara Avenue ͓DOI: 10.1117/1.2769018͔ Las Vegas, Nevada 89117 Subject terms: gemstone evaluation; gemstone grading; gemstone brilliance; gemstone fire; gemstone scintillation; gemstone cuts; round brilliant; gemstones; diamond cuts; diamonds. James Caudill American Gem Society Advanced Instruments Paper 060668R received Aug. 28, 2006; revised manuscript received Feb. 16, 8881 West Sahara Avenue 2007; accepted for publication Apr. 10, 2007; published online Oct. 1, 2007. Las Vegas, Nevada 89117

Peter Yantzer American Gem Society Laboratories 8917 West Sahara Avenue Las Vegas, Nevada 89117

1 Introduction are refracted out of the stone. Each beam generation carries Craftsmanship of gemstones that produce appealing illumi- less and less energy according to the Fresnel coefficients, to nation effects has been an endeavor of the gem cutting light absorption in the bulk of the gemstone material, or to industry throughout its history. Early gem cutters found that light scattering by material inclusions. Light that exits the by properly designing and cutting a gem, especially clear gemstone may reach the eyes of an observer creating a diamonds, it was possible to capture light from above the plurality of illumination effects that significantly impact the gem and redirect it to the eyes of an observer. Gems are appearance of the gemstone. Among the most important produced with a variety of cuts that comprise a plurality of and long-recognized1 effects are gem brilliance, gem fire, planar surfaces called facets. The top facets form the crown gem scintillation, and gem leakage. Historically there have and the bottom facets form the pavilion of the stone. The been several definitions of these effects that capture their facets themselves are polygonal in their boundary. Facets in essence. For example, brilliance refers to the ability of a the crown capture light and facets in the pavilion reflect stone to redirect light to the eyes of an observer so that the light by total internal reflection. This light capturing and gem’s crown appears illuminated. The effect of fire refers redirection function makes a gem appear illuminated and to the rainbow-like colors with which light exits a gem’s there are several illumination effects produced that make a facet as seen by an observer. Fire occurs because white stone appealing. The main illumination effects are bril- light entering or exiting a stone is dispersed into its con- liance, fire, and scintillation. There is a limited set of cuts stituent colors. The effect of scintillation refers to flashes of that favor the simultaneous presence of these effects that light, white or colored light, that are produced when the produce what is known in the trade as the life of a gem- gem, the observer, or the illumination source move. Scin- stone. Defining and quantifying brilliance, fire, and scintil- tillation is a dynamic and rich effect. The effect of leakage lation is relevant in the gem cutting industry where gem refers to light that exits the stone through the gem pavilion grading schemes are important for establishing value to rather than through the crown and may not contribute posi- gemstones and for informing the consumer. tively to the gemstone appeal. When a beam of light enters a gemstone it is split and A primary goal in gem cutting is to maximize the carat partitioned by the stone facets into a plurality of beams that weight of a given stone to be cut; however, recently there are totally internally reflected and then refracted out of the has been an emphasis in also maximizing the illumination stone. The refracted beams, through Fresnel splitting, create appeal of gems. The illumination effects produced by gems second and higher-order generations of beams that in turn have been traditionally evaluated with the unaided eye and with the aid of magnifiers. The first device to be recognized 0091-3286/2007/$25.00 © 2007 SPIE as an effective tool to aid in the cutting of stones is the

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Fig. 3 Nomenclature to indicate ray directions. Normal to the gem table ͑the axis of the gem͒ is 90 deg and parallel to the table is 0 deg.

about gemstone symmetry and brilliance, and the Angular Spectrum Evaluation Tool ͑ASET͒4 device, designed to show critical directions from which a gem captures light. Previous studies1,5–8 have been fruitful in understanding illumination effects in gemstones but have been limited in scope due to the lack of computing power. The develop- ment of nonsequential ray tracing software, commercial and company-proprietary, along with the ability to repre- Fig. 1 Nomenclature of the round brilliant cut. sent digitally and in detail the geometry of a given gem- stone has resulted in the ability to model and evaluate gem- stones with significant realism. For example, it is possible 9 ® 2 to design gems in a computer ͑GemCad ͒, model their ap- FireScope , which was invented in Japan in 1984 and de- ͑ 10͒ signed to judge brilliancy of precious stones. It is a simple pearance under different lighting conditions DiamCalc , and trace rays to extract other useful information ͑ASAP,11 device that uses a small cap painted internally red, a dif- 12 13 14 15͒ fused white light source, and 10X eyepiece. Other devices Fred, LightTools, TracePro, and ZEMAX . Given for gemstone evaluation have been invented such as the the ability for modeling gems in a computer there have Gilbertson3 instrument, designed to provide information been some interesting and useful studies of the round bril- liant diamond as performed by the Gemological Institute of America16,17 and Moscow State University.18,19 Recently there has also been progress in understanding the illumina-

Fig. 4 Angular spectrum of a round brilliant as projected in the hemisphere. Each dot represents a ray direction that can make a Fig. 2 Light rays can enter the gem and be redirected to the eye virtual facet appear illuminated. Several ray refractions, including from different directions. the primary, are included.

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Fig. 7 ͑a͒ Cut facets, ͑b͒ virtual facets upon the primary refraction as projected on the crown in the face-up position, and ͑c͒ virtual facets upon the primary and secondary refraction in the face-up position.

2 Gemstone Nomenclature Fig. 5 Angular spectrum of a round brilliant as projected in the In the jewelry industry there is a terminology to designate hemisphere. Only the primary refraction is displayed. different portions or regions of a given gemstone and for the purpose of this paper it is appropriate to review the 4,20–22 most significant entities as they pertain to the geometry of a tion effects in gemstones, in improving the cutting of gemstone. A gemstone is divided into regions comprising stones to exacting dimensions, and in development of better 23,24 flat surfaces called facets as shown in Fig. 1 in cross section tools for gem cut metrology. for the round brilliant diamond. The crown is the top por- In view of this progress, there is a renewed interest in tion of the stone, which in turn is divided into the table and the gemstone industry for grading gems based on their per- the bezel. The bezel contains the eight star facets, eight kite formance ͑illumination attributes͒ rather than in cut propor- facets, and sixteen upper girdle facets. The pavilion is the tions as has primarily been done for many decades. A grad- lower portion of the stone and is divided into the lower ing scheme based on illumination performance requires girdle facets, the pavilion main facets, and the culet. The characterization approaches that can quantify the light han- girdle separates the crown and the pavilion and comprises a dling abilities of gems. The American Gem Society has plurality of significantly smaller facets that are parallel to been engaged in producing a simple, consistent, and realis- the main axis of the stone. The axis of the stone passes tic approach to the optical testing and characterization of through the center of the culet and it is perpendicular to the gemstones, which is the subject of this paper. The primary table. For the case of the standard round brilliant cut dia- goals of this study are to define and evaluate the illumina- mond there are 58 facets, 33 in the crown and 25 in the tion attributes in gems of brilliance, fire, and scintillation. pavilion. The approach uses an instrument, called the Angular Spec- The standard round brilliant is one out of a plurality of trum Evaluation Tool ͑ASET͒, for the direct optical testing cut possibilities within the round shape. There are many of real gemstones, including fancy shapes, and ray tracing other important cut geometries such as the emerald, prin- through virtual gemstones. The study presented here dis- cess, oval, pear, and marquise cuts, which are known in the cusses the round brilliant cut. We introduce evaluation trade as fancy cuts. Each cut has their own myriad of varia- maps that include angular spectrum maps, dispersion maps, tions that produce different illumination effects to the ob- scintillation maps, and glare maps. These maps simplify the server. evaluation of gemstones and are a valuable educational tool. 3 Geometrical Angular Spectrum and Structured Illumination One insightful approach to analyzing illumination effects in gems is to utilize the concept of geometrical angular spec- trum. The angular spectrum can be considered as a gem signature and intrinsically carries the cut proportions. Here

Fig. 6 ASET Map of a round brilliant gem coded by colors on the Fig. 8 The Gabrielle cut ͑a͒ and its virtual facets ͑b͒ upon the pri- gem’s crown according to angular ranges. mary refraction.

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Fig. 9 ASET Map of the Tolkowsky cut upon the primary refraction. Gray areas represent light leakage. angular spectrum refers to the set of ray angle directions that can make the facets of a gem appear illuminated. For a given position of a gem in relation to an observer there is a Fig. 10 ͑a͒ ASET ͑left͒ and gray-scale ͑right͒ map of a round brilliant ͑ ͒ ͑ ͒ ͑ ͒ set of directions with which rays can enter a gem and be cut that is brilliant, and b ASET left and gray-scale right map of a cut that shows little brilliance. directed to the observer’s eye. An entering ray will be first split into two due to Fresnel reflection. The reflected ray will be considered as contributing to glare if it reaches the observer’s eye. The refracted ray will be internally reflected ance. The concept of angular spectrum is helpful to de- until it is refracted out of the gem and will contribute to couple the contributions to a gem’s appearance from the brilliance and fire if it reaches the observer’s eye. This ray illumination conditions and its cut. It would be possible to upon exiting will be split and the resulting reflected ray will arrange the illumination conditions to make many gems continue to be refracted and split. Thus the angular spec- appear with the attributes of brilliance, fire, and scintilla- trum of a gem contains ray directions corresponding to a tion. In practice the illumination conditions are not ideal first generation of rays split only once upon exiting the gem and therefore under the average illumination conditions, ͑known as primary refraction͒, a second generation of rays only a limited set of cuts will exhibit those illumination split twice ͑known as secondary refraction͒, and other- attributes in a significant manner. higher ray generations according to the number of ray It can be stated that the visual appeal of a gemstone is splits. The first ray generation will contain most of the en- related to the variety of illumination effects that it can pro- ergy of the original entering rays. Successive ray genera- duce. A gemstone that appears evenly illuminated with no tions will contain significantly less energy. For the case of fire or scintillation attributes has little appeal. To produce diamond that has an index of refraction of 2.4 about 83% of brilliance, fire, and scintillation the illumination must be the energy remains in the refracted ray and about 17% in structured and this can be achieved in three manners. The the reflected ray. Materials with a lower index of refraction first is by the illumination conditions of the environment will contain more energy in the refracted ray. Thus the pri- where the stone is observed; the second is by the partial mary refraction accounts significantly for the appearance of obscuration of the gem’s angular spectrum by the observer, a gem. and the third manner is by the intrinsic properties of the cut. The appearance of a gemstone depends not only on a Structured lighting is a key concept for understanding and gem’s cut geometry, which determines the angular spec- producing illumination effects in gemstones and it is em- trum, but on the illumination conditions. For example, dif- phasized in this paper. fuse illumination will favor brilliance and localized illumi- nation, such as spot lighting, will favor fire and flash 4 Angular Spectrum Acquisition and Display scintillation. Regardless of the illumination, each illumina- Figure 2 shows the eye of an observer, a gemstone, and two tion distribution will have associated an angular spectrum rays that reach the eye of the observer upon the primary and the product of the angular spectrums of the illumina- refraction. Each ray has a particular direction and the set of tion and the gemstone will determine the stone’s appear- directions of rays that reach the observer’s eye constitutes

Fig. 11 The phenomenon of dynamic contrast shown in a series of tilt positions ranging from −30 to 30 deg in 5-deg intervals.

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crown are coded by color ͑green low angles, red medium angles, and blue high angles͒. Gray regions represent light that leaks through the pavilion and therefore do not contrib- ute to brilliance or fire. This representation of the angular spectrum by ranges and zones on a gem’s crown is useful because it directly relates ray directions to crown zones and therefore can be easily interpreted. We call this graphical representation of the angular spectrum an ASET map. The choice of the angular ranges to acquire the angular spectrum reflects practical considerations. The high angles range ͑blues͒ is set from 75 to 90 deg because the head of Fig. 12 ASET maps of the Tolkowsky cut with 30 ͑left͒ and 40 ͑right͒ an average observer can block this angular range. Thus deg of obscuration ͑blues͒ for the high angles. The 40-deg ASET upon the face-up position the blues represent areas in a map shows the added blue regions with a darker hue. gemstone that may not receive light due to the obscuration of the observer’s head. The medium angles ͑reds͒ are set from 45 to 75 deg. This choice comes from four consider- the angular spectrum of the primary refraction. The dis- ations: first is the knowledge of the angular spectrum of tance at which the eye is positioned with respect to the gemstones that are brilliant, second is the fact that observa- stone is set to 250 mm from the stone table and along the tion of gemstones is naturally done with light arriving ei- axis of the stone. This observation geometry is called the ther from the back or above the head of the observer, third face-up position. Other observation geometries that involve is the structured lighting that is created in the gemstone due tilting the stone are called tilt positions. A hemisphere of to the obscuration of the head and body when the stone is in radius 250 mm with its center in the girdle plane is a useful movement, and fourth is that in realisitic environments il- reference to indicate ray directions. The axis of the stone lumination frequently occurs at angles greater than 45 deg. passes through the center of the hemisphere and ray direc- The low angles range ͑greens͒ is set from 0 to 45 deg as it tions are measured with respect to the plane of the table. does not contribute significantly to brilliance or structured Thus a direction of 90 deg coincides with the axis of the lighting. There is some simplification in the ranges selected stone and hemisphere as shown in Fig. 3. that intends to account for common illumination and obser- One way to acquire the angular spectrum of a gem is vation conditions. Increasing the number of angular ranges through computer modeling and ray tracing. Rather than would provide more information at the expense of practical forward illuminating the gem, a reverse ray trace starting at simplification. For example, ASET maps with variations in the observer’s eye will indicate the ray directions that ac- the tone of the three main colors according to further angu- tually can bring light to the observer’s eye. If these ray lar subdivision can add useful information. The three angu- directions are projected into the hemisphere, then a 2-D lar ranges in elevation are deemed to be appropriate for the map as shown in Fig. 4 can be produced. This map shows purposes of the characterization approach presented in this the ray directions or angles that can contribute to brilliance paper. Given the eightfold symmetry of the round brilliant and fire. In this 2-D map each dot represents a particular cut there is no need to further subdivide the angular ranges ray direction. The map includes several generations of ray in the hemisphere with respect to azimuth. Some fancy cuts splits and shows the richness of the angular spectrum given with reduced symmetry, however, would require further the Fresnel ray split. In comparison, Fig. 5 shows the an- subdivision of the hemisphere to acquire more detailed in- gular spectrum contributed only by the primary refraction. formation about their angular spectrum. In this later case there is a one-to-one mapping between the direction and the point where a ray exits the gem’s crown in its path to the observer’s eye. 5 Illumination Effects Although reverse ray tracing can easily display a precise The main goal of this paper is the evaluation of the illumi- representation of the angular spectrum in the hemisphere, it nation effects of brilliance, fire, and scintillation. However, is more insightful to actually show regions in the gem’s a full understanding of these desirable effects requires tak- crown that contribute to specific angular spectrum ranges. ing into consideration other effects. Therefore in this sec- We have defined three angular ranges in relation to the tion we review the illumination effects of virtual facets, surface of the table in the stone crown: low angles are from brilliance, contrast, fire, scintillation, leakage, and glare, 0 to 45 deg, medium angles from 45 to 75 deg, and high and introduce maps that permit their evaluation. The struc- angles from 75 to 90 deg. Figure 6 shows the appearance of tured lighting in these maps is conveyed by the spatial dis- a gem when the angular ranges as projected in the gem’s tribution and variety of colors in the maps as commented

Fig. 13 Brilliance of a round brilliant stone as the illumination over the hemisphere increases in 30-deg sectors. Note that by 180 deg the crown is substantially illuminated and exhibits positive contrast properties.

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Fig. 14 How light dispersion and the clipping of the eye pupil can Fig. 16 Rays from a large source can recombine to produce a non- produce a colored appearance of a small facet. ͑A͒ eye, ͑B͒ virtual colored, white appearance of a facet. ͑A͒ eye, ͑B͒ virtual facet ap- facet appearance, ͑C͒ small aperture, ͑D͒ prism, ͑E͒ light source, pearance, ͑C͒ small aperture, ͑D͒ prism, ͑E͒ light source, and ͑F͒ and ͑F͒ virtual source image. virtual source image. below. By design, the bezel in a gemstone has more struc- as virtual facets and their number depends on the number of ture than the table and therefore the bezel exhibits more actual facets the stone has and on the number of times light illumination effects. is partitioned as it propagates in the stone. Within the round shape there are cut geometries that include more facets than ® 5.1 Virtual Facets the standard round brilliant cut such as the Gabrielle cut. This cut is shown in a solid view and with its virtual facets The observation of a gemstone reveals that its appearance upon the primary refraction in Fig. 8. The size and distri- consists of many more facets than the actual number of cut bution of the virtual facets have an impact on the visual facets. This occurs because as a beam of light enters a appeal of a stone. If the size of the virtual facets approaches gemstone it is divided into a plurality of beams resulting the limit of the eye’s resolution then fire and flash scintil- from the projection of the entering beam on the gemstone lation will tend to appear as pinpoint events. If the size of facets as shown in Fig. 7. These perceived facets are known the facets is several times larger than the eye’s resolution then the effect of facet interplay can be observed. This ef- fect is desirable and consists of the sudden change of ap- pearance of groups of alternate facets becoming dark, illu- minated, or colored. Facet interplay is reminiscent of the sudden changes in pattern produced by a kaleidoscope when it is in movement. Upon secondary refraction, further beam partitioning takes place and the virtual facets become smaller, as is also shown in Fig. 7. The small virtual facets upon secondary and higher-order refractions contribute to pinpoint fire and scintillation. The first refraction mostly contributes large virtual facets, which are key in producing facet interplay. Thus the primary refraction is the most significant because of the amount of light it carries and the size of the virtual facets.

5.2 Gem Brilliance Gemstone brilliance refers to the ability of a stone to appear illuminated to an observer. For this to occur light must be directed from the virtual facets to the observer’s eyes. In this paper we measure the illumination effect of brilliance by the observed area of the crown that can direct light from Fig. 15 A large facet can appear multicolored since it can redirect to the eye dispersed light from different locations in the facet. ͑A͒ eye, the medium angles to the observer’s eye. Figure 9 shows ͑B͒ virtual facet appearance, ͑C͒ large aperture, ͑D͒ prism, ͑E͒ light the primary angular spectrum of the Tolkowsky cut as pro- source, and ͑F͒ virtual source images. jected in a stone crown. For this cut, 20.5% of the crown is

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Fig. 17 Angular spectrum of a gemstone as projected in the hemisphere upon −15, −10, −5, 0.0, 5, 10, and 15 deg tilts. This sequence shows that upon tilting a stone the probability of intersecting a source by the angular spectrum is essentially one.

illuminated with light from the high angles ͑blues͒, 67.0% 5.3 Gem Contrast ͑ ͒ with light from the medium angles reds , 7.2% with light The high angular range as represented by blue color in an ͑ ͒ from the low angles greens , and 5.3% of the light is not ASET map indicates the zones in a stone crown that are not redirected to the observer’s eyes due to leakage. illuminated due to the obscuration of the observer’s head. Under broad diffuse illumination the crown of a stone This obscuration produces what is known in the trade as may substantially appear evenly illuminated. However, if gem contrast.19,20 In proper amount and distribution, con- the illumination environment is structured and comprises trast creates structured lighting that enhances brilliance, several sources of white light that have an appreciable an- fire, and scintillation. Contrast can be a detrimental effect if gular subtend, of a few degrees to a few tens of degrees, it is significantly localized. Too little contrast results in a then some virtual facets would appear white and bright stone appearance lacking variety under broad diffused illu- while others would appear translucent or dim. When a vir- mination. Too much contrast results in a stone that lacks tual facet is illuminated it appears to the observer as if it is brilliance. The combination of positive contrast character- a light source by itself. istics and brilliance properties in a gemstone is known as For understanding the illumination appearance of a gem contrast brilliance. it is useful to think of a gem’s facets and their optical pro- When a gemstone is in movement the contrast pattern jections, the virtual facets, as a collection of tiny prisms changes in form. This effect is called dynamic contrast and that direct light to an observer’s eyes. Thus brilliance in this adds substantial appeal to the appearance of a stone as stati- ͑ ͒ paper is defined as the percentage by area of such tiny cally shown in Fig. 11 with a series of tilt maps ranging prisms that can direct light to the observer’s eyes. This from −30 to 30 deg in 5-deg intervals. definition is simple and does not intend to account for Contrast, as represented by the blue region in the ASET obliquity factors that could be included to account for dif- maps, is acquired by blocking a cone of 30 deg in the an- ferences in the relative position of facets or illumination gular spectrum. Additional information about contrast is conditions. For example, in typical illumination scenarios obtained by increasing the angular spectrum obscuration to the relative intensity of light provided by light sources var- 40 deg. This increased obscuration represents having the ies significantly from place to place. This makes the inclu- observer looking closer at the stone, closer than 250 mm, sion of obliquity factors substantially irrelevant. In addi- and it is used to critically evaluate the contrast properties of tion, the definition is congruent with the intuitive idea that gemstones in the face-up position. Figure 12 shows the something brilliant is an object that can direct light to an ASET maps for the Tolkowsky cut with 30 and 40 deg of observer’s eye. Thus a gem is said to have the attribute of obscuration. The fact that the Tolkowsky cut retains a well- brilliance if it can direct light to the observer’s eyes. Effec- balanced contrast pattern in these two views indicates su- tively, a brilliant gem can be equated with a structured light periority in creating structured lighting. Thus characterizing source. Figure 10 shows the ASET and gray-scale maps of gem contrast is essential in assessing the visual appeal of a round brilliant cut that is deemed to be brilliant and one gemstones. that is not. The perception of brilliance also depends on the background as it is discussed next.

Fig. 19 ͑a͒ Forward fire map, ͑b͒ reverse fire map, and ͑c͒ key: gray indicates obscured, low-angle light or leakage. Dark orange indi- cates a linear dispersion of 2.0 mm or less at the eye of the observer ͑forward map͒ or at the source ͑reverse map͒. Orange is dispersion between 2.0 mm and 4.2 mm, light orange is dispersion between Fig. 18 The bigger the chromatic flares are, the larger the probabil- 4.2 mm and 6.4 mm, and yellow is dispersion larger than 6.4 mm for ity is of being captured and clipped by the eye’s pupil. the chosen wavelengths of 420 and 620 nm.

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Fig. 21 Illumination key in the hemisphere with ͑a͒ concentric illu- Fig. 20 Scintillation maps of a round brilliant with ͑a͒ concentric ͑ ͒ ͑ ͒ mination over the medium angles, and b sector illumination over illumination and b sector illumination. Concentric illumination the medium angles. The colors used are red, green, blue, cyan, shows how the virtual facets are illuminated as a source scans ra- magenta, and yellow. dially the hemisphere. Sector illumination shows how the virtual fac- ets are illuminated as a source scans in azimuth the hemisphere. subtend of the facet is small, then only one color would be observed across the facet. As the angular subtend of the An alternate view to contrast properties is shown in Fig. facet increases, more colors would be observed, until fi- 13 where the hemisphere increases its illumination as the nally the entire spectrum would be seen. Essentially, the azimuth range is increased from zero to 360 deg in 30-deg eye would be observing the source at different lateral loca- increments and upon the face-up position. tions depending on the color as shown in Fig. 15. The facet size would be large enough to permit the eye to see the 5.4 Gem Fire source at those different locations. However, gem facets are The phenomenon of fire is one of the most appealing ef- typically small so that in the presence of fire they appear fects in transparent gemstones. Under favorable conditions substantially with a single color. fire makes individual facets appear fully colored with the As the angular size of the source increases from a small rainbow hues.25,26 Fire inherently occurs due to the light fraction of a degree to a few degrees the color saturation dispersion upon refraction as light enters and exits a stone. will decrease. Intermediate colors such as green will disap- Three factors determine the amount of fire perceived from a pear first, then only blue and red will be observed, and facet, namely, the angular dispersion of light upon refrac- finally no colors will be observed. In this process of in- tion from the gemstone, the angular subtend of the source, creasing the source size, ray overlap from different loca- and the angular subtend of the eye’s pupil in relation to the tions in the source takes place, washing out the colored facet. appearance of the facet as shown in Fig. 16. To best observe fire it is required to have a localized Modeling of gem fire can be done by assuming specific source of light so that its angular subtend is much smaller localized illumination scenarios such as spot lighting or than the angular dispersion produced by the gem facet, es- chandelier illumination. However, gem evaluation may fa- sentially a point source. As different colored rays arrive to vor certain cuts that perform better in those specific illumi- the eye from a facet, some of them enter the eye’s pupil and nation conditions. The approach to characterize fire fol- others are blocked producing a colored appearance of the lowed in this paper is based on the observation that the facet as shown in Fig. 14. In this process the boundary of angular spectrum of most realistic cuts is rich. When a the eye’s pupil plays a critical role in obstructing portions gemstone is in movement, for example, tilted back and of the spectrum to achieve the colored facet appearance. At forth, its angular spectrum scans the hemisphere, resulting 250 mm of distance and considering the dispersion of dia- in essentially a probability of one to intersect a given local- mond, which is on the order of 0.044, wavelengths at 420 ized light source. This observation is illustrated in Fig. 17, and 620 nm can be linearly spaced up to several millime- which shows the angular spectrum of a gemstone that has ters by a gem. Depending on the illumination conditions been tilted in the range of ±15 deg with respect to the and the age of the observer, the human pupil size can range face-up position. The practical meaning of this observation from about 2 to 8 mm in size. Therefore there is some is that for evaluating fire one can factor out the illumination variability on the amount of fire perceived by different ob- conditions. Thus, our evaluation of fire is independent of servers in different illumination conditions. the source distribution. Appendix A provides further sup- Relative to the eye’s position, the angular subtend of a port with a study of the angular spectrum as a function of given facet determines the appearance of the facet. If the stone cut parameters.

Fig. 22 Glare maps of a round brilliant showing directions in the hemisphere that can contribute glare. The maps are in tilt positions ranging from −30 to 30 deg in 5-deg intervals.

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Fig. 23 A matrix of ASET maps as a function of crown and pavilion Fig. 24 ASET matrix with 40 deg of obscuration upon primary re- angles upon primary refraction. The highlighted diagonal lines rep- fraction. ͑High-resolution image available online only. ͓URL: resent the main cutter’s line ͑slope of −1͒ and the anti-cutter’s line http://dx.doi.org/10.1117/1.2769018.2͔͒ ͑slope of +1͒. Note that illumination properties are similar along lines parallel to the main cutter’s line. ͑High-resolution image available online only. ͓URL: http://dx.doi.org/10.1117/1.2769018.1͔͒ 620 nm. Fire maps are produced by tracing two rays per crown position at different wavelengths and noting the amount of dispersion. Two fire maps, for each stone geom- Then, the next important factor in the production of fire etry, can be produced depending on the use of reverse is the amount of dispersion that rays from facets in a gem’s ͑from the eye to the source͒ or forward ͑from the source to crown have. Gemstones at a distance of 250 mm possess the eye͒ ray tracing. Forward fire maps, produced in the barely enough dispersion ͑on the order of millimeters͒ to observer’s space, show the potential to observe fire. Re- separate the light colors across the observer’s pupil. The verse fire maps, produced in the source space, show the amount of dispersion from each virtual facet is a significant potential to observe a source. The dispersion in the reverse measure of fire. The larger the dispersion from a facet, the and forward fire maps is related by the anamorphic magni- higher the probability will be that the eye’s pupil will clip fication associated to the prism corresponding to each vir- dispersed rays to produce a colored appearance as shown in tual facet. Fig. 18. When there is a larger amount of dispersion, the There are other factors that can determine fire in a gem- color perceived will be purer ͑more color saturation͒ but stone, as for example the amount of light from higher-order with a decrease in intensity. The decrease in color intensity refractions that coincide with the primary refraction upon is not a concern due to the relatively high brightness of exiting the gemstone. The structured lighting that results localized sources that can produce fire. from dynamic contrast and the inherent light scrambling Figure 19 shows what we call a fire map, which indi- inside the gemstone are other factors that count. However, cates the potential of a stone to produce fire. It is actually a the fire maps upon primary or higher-order refractions dispersion map, coded by colors, that indicates the amount ͑those that result from Fresnel ray split͒ convey signifi- of dispersion that a white-light ray will undergo in reaching cantly the fire potential of a stone and are a valuable tool the observer’s eye at a distance of 250 mm in the face-up for assessing gem fire. position. Dark orange indicates a linear dispersion of 2.0 mm or less at the eye of the observer. Orange is disper- sion between 2.0 mm and 4.2 mm, light orange is disper- 5.5 Gem Scintillation sion between 4.2 mm and 6.4 mm, and yellow is dispersion In the presence of brilliance and fire the most appealing larger than 6.4 mm for the chosen wavelengths of 420 and effect is gem scintillation. In this effect the fire pattern

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Fig. 25 ASET matrix upon secondary refraction. ͑High-resolution Fig. 26 ASET matrix produced with one half of the illumination image available online only. hemisphere. ͑High-resolution image available online only. ͓URL: ͓URL: http://dx.doi.org/10.1117/1.2769018.3͔͒ http://dx.doi.org/10.1117/1.2769018.4͔͒ changes dynamically and flashes of white light are per- ceived across the crown of the stone. Thus there are two stone. These light scrambling properties of a stone are the major scintillation effects, fire and flash scintillation. To third mechanism to produce structured lighting. In this pa- observe them it is required that the stone, the observer, or per we define the light scrambling properties of a stone as the illumination conditions be in movement. Typically the its ability to mix or scramble its angular spectrum as it is observer tilts the stone back and forth to observe scintilla- projected into the stone crown. In particular, attention is tion and naturally optimizes for the direction that maxi- paid to the scrambling of the medium angular range or reds mizes scintillation. Without brilliance, as defined in this in the ASET maps. paper, there cannot be fire since no light can be brought to Figure 20 shows what we call scintillation maps. These the observer’s eyes. Without fire there cannot be fire scin- maps are generated with light reaching the observer’s eye tillation as defined by the change of fire pattern. Flash scin- in the face-up position from the medium angles, 45 to tillation can occur without fire scintillation and it is due to 75 deg, in the hemisphere and in a 60-deg sector as shown light sources not small enough in angular subtend to pro- in Fig. 21. They are presented in six colors ͑red, green, duce fire, or to the inability of a stone to sufficiently dis- blue, cyan, magenta, and yellow͒ to further subdivide the perse light for a given position of the observer. White dif- medium angles into regions that are concentric arc circles fused illumination will wash out both scintillation effects. or truncated pie sections. The interpretation of the scintil- Sources that subtend a small angle will contribute more to lation maps is different than the ASET maps. Recall that in produce a flash effect, the rapid turn on and off of the light the ASET maps colors indicate the ray directions that can from a given facet, than sources that subtend larger angles. make a stone crown appear illuminated. The scintillation Thus fire scintillation is more vivid than flash scintillation. maps represent the change in illumination of the crown as a The amount of gem scintillation perceived is linked to light source scans, in azimuth or radially, the medium the brilliance and fire of a stone. However, scintillation angles in the hemisphere. A stone deemed to substantially strongly depends on the change of illumination conditions. scramble light would appear with the colors well distrib- This change is primarily produced on purpose by the move- uted over its crown in the scintillation map view. In Fig. 20 ment of the stone as it is admired. The effects on scintilla- the size and form of the virtual facets is clearly shown as tion due to the stone movement in turn can be enhanced well as the illumination distribution over the crown of the according to the intrinsic light scrambling properties of the gem. Thus a scintillation map conveys information about

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Fig. 27 Matrix of reverse fire maps upon primary refraction. Fig. 28 Matrix of forward fire maps upon primary refraction. ͑High-resolution image available online only. ͓URL: ͑High-resolution image available online only. ͓URL: http://dx.doi.org/10.1117/1.2769018.5͔͒ http://dx.doi.org/10.1117/1.2769018.6͔͒ the size and form of the virtual facets and about the intrin- sic light scrambling properties of a gem, and hints at how a stone would exhibit scintillation. can produce glare. Glare maps with significant glare from the medium angles ͑reds͒ are deemed undesirable; they cor- respond to stones with shallower crown angles. 5.6 Gem Leakage Gem leakage refers to areas in the pavilion where total internal reflection does not occur. Consequently and de- pending on the light source, the light intensity from leaky 6 Map Matrices regions may not be as intense as in other regions in the In the previous section we have introduced several maps stone. In addition, in stones that are mounted in pronged that are useful in evaluating and comparing gemstones. mounts it is possible for light to enter through the pavilion This section provides matrices of maps as a function of the and reach the observer’s eye by exiting though the crown. crown and pavilion angles for a given table size of a stan- Upon secondary refraction, leakage areas can also contrib- dard round brilliant cut. In this study the table size is 53%. ute to fire and scintillation given that localized sources are The maps give an ample view of the trade-offs in the cut bright. Leakage can be considered a detrimental effect, space as commented for each map. The horizontal axis cor- though it is possible that small amounts of leakage that are responds to the crown angle ranging from 24.5 deg ͑left͒ to well distributed may add variety to the illumination effects 38.5 deg ͑right͒ with 1.0-deg intervals. The vertical axis in a positive manner. corresponds to the pavilion angle ranging from 38.5 deg ͑bottom͒ to 43.5 deg ͑top͒ with 0.2-deg intervals. The maps 5.7 Gem Glare are generated with the primary refraction except as indi- Gem glare results from the reflection of a light source on cated for some ASET and fire maps. It will become appar- the surface of crown facets. This light does not enter the ent that the matrices show certain important trends in illu- stone and hides the appreciation of the main illumination mination properties. The Tolkowsky cut is a reference cut effects that are perceived inside the stone. Figure 22 shows and is located at P41.7/C34.5 where P41.7 indicates a pa- a series of glare maps that indicate, upon the face-up posi- vilion angle of 41.7 deg and C34.5 a crown angle of tion and tilt positions, the directions in the hemisphere that 34.5 deg.

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Fig. 29 Matrix of reverse fire maps upon secondary refraction. Fig. 30 Matrix of forward fire maps upon secondary refraction. ͑High-resolution image available online only. ͓URL: ͑High-resolution image available online only. ͓URL: http://dx.doi.org/10.1117/1.2769018.7͔͒ http://dx.doi.org/10.1117/1.2769018.8͔͒

6.1 ASET Maps from an N-dimensional to an ͑N−1͒-dimensional analysis. Figure 23 shows a matrix of standard ASET maps ͑30 deg Both the main cutter’s line and the anti-cutter’s line are of obscuration͒ in the face-up position for the round bril- highlighted in the matrices. liant cut. The matrix shows that there is a trade-off between The ASET maps are the most important descriptors of crown angle and pavilion angle. That is, a crown change of illumination performance given that they characterize bril- 1 deg can be traded-off by a pavilion angle change of about liance and contrast. The maps with significant reds and 0.2 deg to maintain the same properties to within some lim- some well-distributed blues are the stones that are deemed its. As far as brilliance is concerned this trade-off has been to perform the best. The stones on the lower left are bril- known in the industry for some time. What is little known liant but, as discussed below, suffer from some problems. is that the trade-off exists even for other properties as is One of these problems is that upon stone tilt the girdle as shown in the matrices describing other illumination effects. reflected by the pavilion appears in the table. In the ex- Given the steps in the vertical and horizontal axis the stones treme, these types of stones are called fish-eyes. The bril- appear to have similar properties along lines running at liant stones near the Tolkowsky and along the main cutter’s 45 deg ͑slope of −1͒ from top to bottom. The 45 deg ͑slope line are the best performers. Note that the Tolkowsky cut of −1͒ line passing by the Tolkowsky cut is called the main appears to be near a boundary where the stones change cutter’s line. This line gives insight to diamond cutters properties. about how to adjust the crown angle for a given pavilion Stones with significant blues in the table are called nail- angle change and represents a trade-off in stone cutting. heads because the table appears dark due to light retrore- Other lines at 45 deg that are parallel to the main cutter’s flection and/or obscuration upon close examination. The line are called cutter’s lines. A line perpendicular to the stones with significant greens will tend to lack brilliance in main cutter’s line ͑slope of +1͒ and that also passes by the the bezel and structured lighting. Some other stones have Tolkowsky cut is called the anti-cutter’s line. The recogni- significant leakage as shown by the gray regions. tion of the cutter’s trade-off simplifies considerably the The matrix of ASET maps also supports the choice of analysis of gemstones. The main differences in stone be- angular ranges to subdivide the hemisphere. For example, havior within reasonable limits appear along the anti- the low angles ͑greens͒ are mainly distributed over the be- cutter’s line. Thus the cutter’s trade-off reduces the analysis zel and have a poor distribution over the crown of stones in

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Fig. 31 Matrix of scintillation maps upon primary refraction. Fig. 32 Matrix of scintillation maps upon secondary refraction. ͑High-resolution image available online only. ͓URL: ͑High-resolution image available online only. ͓URL: http://dx.doi.org/10.1117/1.2769018.9͔͒ http://dx.doi.org/10.1117/1.2769018.10͔͒

the matrix. The stones in the top right corner of the ASET map matrix are the ones that contribute more low-angle light. Thus low-angle light does not significantly contribute to brilliance or structured lighting. In regard to the high angle ͑blues͒, its distribution and amount can be significant; however, its angular range is essentially set by the extent of the observer’s obscuration. Figure 24 shows a matrix of ASET maps for 40 deg of obscuration, which illustrates how the contrast properties hold or change upon a closer examination of the stone. Note that the only stones that exhibit a positive contrast pattern change are the ones near the Tolkowsky cut along the main cutter’s line. Other cuts like the nail-heads de- velop excessive contrast. Some of the cuts with no contrast remain without contrast. The ASET maps with 40 deg of obscuration also convey the structured lighting abilities of gems. Figure 25 shows a matrix of ASET maps upon the sec- ondary refraction. The main feature of this matrix is that it shows that cuts along the main cutter’s line remain brilliant upon the secondary refraction. In addition, the contrast properties also remain positive. Stones along the anti- cutter’s line change significantly in their contribution to brilliance. The shallow crown, shallow pavilion stones on Fig. 33 Tilt view matrix of ASET maps upon primary refraction the left corner are not considered brilliant upon the second- along the anti-cutter’s line. ͑High-resolution image available online ary refraction given that they contribute light from the only. ͓URL: http://dx.doi.org/10.1117/1.2769018.11͔͒

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Fig. 34 Tilt view matrix of forward fire maps upon primary refraction Fig. 36 Tilt view matrix of scintillation maps upon primary along the anti-cutter’s line. ͑High-resolution image available online refraction along the anti-cutter’s line ͑sector illumination͒. only. ͓URL: http://dx.doi.org/10.1117/1.2769018.12͔͒ ͑High-resolution image available online only. ͓URL: http://dx.doi.org/10.1117/1.2769018.14͔͒

Fig. 35 Tilt view matrix of scintillation maps upon primary refraction along the anti-cutter’s line ͑concentric illumination͒. ͑High-resolution Fig. 37 Tilt view matrix of ASET maps upon primary refraction image available online only. along the cutter’s line. ͑High-resolution image available online only. ͓URL: http://dx.doi.org/10.1117/1.2769018.13͔͒ ͓URL: http://dx.doi.org/10.1117/1.2769018.15͔͒

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Fig. 38 Tilt view matrix of forward fire maps upon primary refraction Fig. 40 Tilt view matrix of scintillation maps upon primary refraction along the cutter’s line. ͑High-resolution image available online only. along the cutter’s line ͑sector illumination͒. ͑High-resolution image ͓URL: http://dx.doi.org/10.1117/1.2769018.16͔͒ available online only. ͓URL: http://dx.doi.org/10.1117/1.2769018.18͔͒

lower angles ͑greens͒. Note also that the pavilion-crown angle trade-off holds to a lesser extent upon the secondary refraction. A useful modification of the ASET maps is the half- ASET map produced with half the hemisphere obscured. Figure 26 shows a matrix of half-ASET maps. Under half- hemisphere illumination the structured lighting produced by the intrinsic properties of the cut are revealed. Stones at or near the main cutter’s line retain positive contrast char- acteristics. Other stones, as for example the shallow crown, shallow pavilion stones, exhibit a half nail-head contrast pattern and lack brilliance. The stones on the top right cor- ner of the matrix lack brilliance in the bezel and are leaky.

6.2 Fire Maps Figures 27 and 28 show matrices for reverse and forward fire maps, respectively. The reverse fire map shows the po- tential to observe a light source given that the chromatic flare ͑the spread of light into a spectrum͒ covers a larger area in the hemisphere, which increases the probability of intersecting a given light source. The forward fire map shows the potential to observe fire given that the larger the chromatic flare, the larger the probability is that the eye’s pupil would clip and capture light from a facet. Forward fire maps are considered the main tool to assess the gem’s intrinsic fire potential ͑without considering the source dis- tribution and observer͒. Both reverse and forward fire maps maintain the trade- Fig. 39 Tilt view matrix of scintillation maps upon primary refraction along the cutter’s line ͑concentric illumination͒. ͑High-resolution off between crown and pavilion angles along the cutter’s image available online only. lines. The stones that exhibit significant fire are along the ͓URL: http://dx.doi.org/10.1117/1.2769018.17͔͒ main cutter’s line. These stones have the property of exhib-

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Fig. 41 ͑A͒ Forward and backward tilts in relation to the observer and source, and ͑B͒ left and right tilts in relation to the observer and source.

iting relatively high dispersion in the table. Other stones 7 Tilt Views that have high dispersion are in the lower-left and top-right Although the maps in the face-up position are a primary corners of the fire matrices. However, these stones suffer tool for evaluating gemstones, they do not provide suffi- from not having high dispersion in the table. cient information about the performance of a stone as it The fire matrices show that the old diamond-cutting in- moves. The tilt-view matrices that we present below pro- dustry rule of increasing the crown angle to achieve more vide a view of the gem properties as a function of the tilt fire is not necessarily true. It only significantly applies to with respect to the hemisphere and the observer. The tilt stones at or near the main cutter’s line or about lines pass- views are generated by tilting the stone from −30 deg to ing by other regions such as the left-bottom and top-right 30 deg in 3-deg increments. Figures 33–36 show the tilt corners. views for the round brilliant cut along the anti-cutter’s line Fire results from higher dispersion and this mainly hap- for ASET maps, forward fire maps, and scintillation maps. pens in the stone bezel. Table fire is rare and stones with Figures 37–40 show the tilt views along the cutter’s line. In significant bezel and table fire are considered superior. 27 the tilt views the Tolkowsky cut is highlighted for ease of Some stones that exhibit significant fire are designed with identification. a small table to maximize the bezel area and therefore fire. The scintillation tilt maps are generated by tilting the Figures 29 and 30 show some matrices for reverse and stone along the symmetry line of the illuminating, truncated forward fire maps upon secondary refraction, respectively. pie sector in the hemisphere as shown in Fig. 41. This is The matrix for reverse fire exhibits significantly more dis- equivalent to tilting a stone forward and backward as it is persion than the matrix for forward fire. However, in both observed. The top maps ͑−15 to −30 deg of tilt͒ in the tilt matrices the stones near or at the main cutter’s line appear view correspond to the backward tilts, the middle map to with significant fire potential. the face-up position, and the bottom maps ͑+15 to +30 deg of tilt͒ to the forward tilts. It can be appreciated that the larger number of scintillation events occur upon the face-up 6.3 Scintillation Maps position ͑no tilt͒ and forward tilts to about 15 deg. The Figure 31 shows a scintillation matrix produced upon the scintillation events observed in the tilt maps correspond to face-up position. Each of the virtual facets that captures light from the hemisphere appears colored and this is termed a scintillation event. The first measure of scintilla- tion potential is brilliance ͑reds in the ASET maps͒, given that for scintillation to occur the stone must be able to redirect light to the observer’s eye. The stones that have more well-distributed scintillation events in color and over the stone’s crown have the potential to produce more scin- tillation than stones with lesser events. For example, Fig. 31 shows that stones at or near the main cutter’s line have spatially well-distributed events as compared to other stones. Figure 32 shows a scintillation matrix upon secondary refraction. This matrix shows that the virtual facets become smaller and scintillation may appear as a pinpoint effect upon localized bright sources. Given that light upon sec- ondary refraction is reflected more times inside the stone, the scintillation appears as more rapidly changing com- Fig. 42 Tolkowsky cut, ASET map, lower girdle facets length 60%, pared to scintillation from the primary refraction. star facets length 35%.

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Fig. 43 Tolkowsky cut, ASET map, lower girdle facets length 80%, Fig. 44 Tolkowsky cut, ASET map, lower girdle facets length 90%, star facets length 50%. star facets length 50%.

tion maps the four best round brilliant stones ͑table 53%͒ ͑ ͒ the events that one would observe when the stone is tilted are P40.9/C33.5, P40.7/C34.5 Tolkowsky , P40.5/C35.5, quickly left to right while holding it at a given forward- and P40.3/C36.5. backward tilt position. For completeness of analysis Appendix A provides ad- In the scintillation tilt maps a light source is assumed to ditional tilt matrices along the main cutter’s line and anti- be located above and behind the head of the observer. The cutter’s line. exact location and size of the light source does not change qualitatively the series of scintillation events seen in the tilt 8 The Tolkowsky Cut view maps. These scintillation events are concentrated in Tolkowsky1 described the reasoning that he followed to ar- the table when the stone is tilted forward, spread over the rive at the proportions of one of the best cuts for a round crown as the stone has less tilt, and then appear in the bezel brilliant. In his research he was guided by the proportions ͑left and right bezel areas͒ as the stone is tilted backward. of stones that were known to exhibit superior performance. Thus the tilt-view scintillation maps represent in a color- His research supported the knowledge that cutters, by trial coded manner what an observer would actually see in ex- and error, had generated over time. In his statement “…we amining a stone. The number of events and their distribu- conclude that the correct value for the pavilion angle is 40 tion in the scintillation tilt views indicate the scintillation degrees and 45 minutes and gives the most vivid fire and properties of a stone. greatest brilliancy, and that although a greater angle would The tilt-view ASET maps along the anti-cutter’s line, give better reflection, this would not compensate for the Fig. 33, show that the best performers in terms of contrast loss due to the corresponding reduction in dispersion” it and brilliance are located at the main cutter’s line and pos- becomes apparent that Tolkowsky noted that his cut is a sibly at the left and right adjacent lines. The tilt-view for- compromise between brilliance and dispersive properties. ward fire maps, Fig. 34, indicate that, in terms of fire po- In fact, contrast and scintillation are part of the overall tential, stones in the cutter’s line and in the line to the right balance. The compromise is clearly shown in the tilt views exhibit the best fire. The scintillation tilt views, Figs. 35 along the main cutter’s line. Tolkowsky and the cut industry and 36, show that stones along the main cutter’s line have advocate high dispersion to achieve fire, which is consistent the best scintillation as indicated by the number and distri- with our research and fire maps. From Tolkowsky’s time bution of events. Thus the cutter’s trade-off and the tilt the round brilliant cut has been improved3 by increasing the views permit one to determine the cutter’s line where the girdle thickness, including girdle facets, reducing the culet best round brilliant cuts are located. These cuts are located size, and increasing the length of the lower girdle facets along the main cutter’s line. and star facets. Figures 42–44 show a study in lower girdle The tilt views along the cutter’s line, Figs. 37–40, permit length and star facets. Figure 42 shows the old round bril- one to determine which are the best stones in terms of liant cut with large virtual facets in the table ͑lower girdle illumination performance. The tilt-view ASET maps along facets length 60%, star facets length 35%͒, Fig. 43 shows the cutter’s line, Fig. 37, show that the Tolkowsky cut, the the modern cut with a balanced virtual facet size that favors two to the left ͑P40.9/C33.5 and P41.1/C32.5͒, and the one the effect of facet interplay ͑lower girdle facets length 80%, to the right ͑P40.5/C35.5͒ are the best in terms of contrast star facets length 50%͒, and Fig. 44 shows the round bril- pattern and brilliance. The tilt-view, forward fire maps, Fig. liant cut with thin pavilion mains ͑lower girdle facets 38, indicate that in terms of fire potential the stones in the length 90%, star facets length 50%͒. main cutter’s line, the Tolkowsky, and the next four stones The Tolkowsky cut and other cuts along the main cut- exhibit the best fire. The scintillation tilt-view maps, Figs. ter’s line have some amount of leakage in the bezel. One 39 and 40, show that stones that exhibit the best scintilla- way to reduce or avoid this leakage is by the technique tion are the last seven in the main cutter’s line given the called painting28,29 in which the facet angle between the better distribution of scintillation events at tilts around the upper girdle facets and the kite facets is reduced. Depend- face-up position. Considering the ASET, fire, and scintilla- ing on the length of the star facets, painting can have a

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Fig. 45 ͑a͒ ASET map, ͑b͒ ASET map ͑40 deg of obscuration͒, ͑c͒ forward fire map, and ͑d͒ photo- graph of a high-performing princess cut.

negative impact on dispersion. Stones along the cutter’s corresponding ray-traced computer generated view. Note line can be painted more without negative dispersion ef- the significant match between the real and virtual ASET fects. images. One way to observe dispersion is by creating an illumi- nation scenario with a plurality of white sources32 distrib- 9 Evaluation of Fancy Shape Cuts uted over the illuminating hemisphere. The ASET instru- The methodology developed to characterize illumination ment can be modified to display light dispersion as shown effects discussed below can also be applied to study fancy in Fig. 49. The modification requires placing a plurality of shape gems such as the princess and emerald cuts. Some white light sources over the medium angles in the hemi- fancy shapes have less symmetry than the eightfold sym- sphere. This is actually produced by placing a screen with metry of the round diamond and others more, for example, pinholes in front of a light diffuser and a broad, white-light fourfold and ninefold symmetry. Therefore the angular source. The angular separation of the pinholes in the screen spectrum of some fancy cuts may not be as rich as it is for is about the same as the angular dispersion produced by the the round brilliant cut and additional angular ranges in el- gem. In this manner the colors produced by a single light evation and in azimuth could be necessary to sufficiently source are not washed out by the overlap with colors from assess the illumination properties. It is also possible to have an adjacent source. However, the pinholes are still close fancy cuts with richer angular spectra than the angular enough to essentially always have light from a pinhole il- spectrum of round brilliants. Each fancy cut requires a luminating each virtual facet. An additional aperture in study by itself. However, the maps and concepts developed front of a camera serves the same function as the eye pupil in our research can still be applied for evaluating fancy in clipping colored rays. By closing or opening this aper- cuts. For example, using our methodology we have identi- ture, more or less saturation in the colored facets can be fied a princess and an emerald cut as shown in Figs. 45 and 30,31 achieved. It is not possible to directly generate fire maps. 46 that upon actual fabrication resulted in stones that However, the colors and color saturation in the views gen- displayed superior fire and brilliance. These cuts have not erated are in agreement with fire maps. For example, Fig. been previously known to the industry and their specifica- 50 shows a sequence of photographs of a round brilliant tions are given in Appendix B. where the clipping aperture is varied in size; the corre- sponding fire map is also shown. Note that the actual pho- 10 ASET Instrument tographs show the crown bezel with more saturated colors. This can be explained from the higher dispersion shown in We have developed an instrument called the Angular Spec- the bezel by the fire map. trum Evaluation Tool ͑ASET͒ to practically evaluate gems and demonstrate results obtained by ray tracing of virtual gems. The ASET instrument is shown in Fig. 47 and con- 11 Real Versus Virtual Gemstones sists of a stage where the gem is placed, a hemisphere The study presented in this paper has been done in a com- carrying the colors according to angular range, a light puter using virtual gemstones that are perfect in their pro- source, and a camera. Figure 48 shows an actual photo- portions and symmetry. Real gems are not perfect in their graph through the ASET of a round brilliant gem and its geometry and suffer from several problems such as facet

Fig. 46 ͑a͒ ASET map, ͑b͒ ASET map ͑40 deg of obscuration͒, ͑c͒ Forward fire map, and ͑d͒ photo- graph of a high-performing emerald cut.

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Fig. 49 Modification of the ASET instrument to display fire. Fig. 47 ͑a͒ ASET instrument and ͑b͒ schematic diagram. position and angular misalignment. These misalignments sources themselves. Light directly reflected from the crown reduce gem symmetry and impact the illumination perfor- facets contributes glare and prevents observation of the ef- mance. One problem is that facet misalignment can reduce fects taking place inside the gemstone. Upon movement of the size of the virtual facets to promote pinpoint effects at the gem, typically the tilting of the gem left to right, or the expense of the facet interplay effect. Some light scat- tilting it backward and forward, the effects of dynamic con- tering can also take place at facets that do not meet as trast, flash and fire scintillation, and facet interplay take expected. Nevertheless, well-cut gems do not have signifi- place. Pinpoint fire and pinpoint white flashes are also ob- cant errors to make the analysis in this paper unrealistic. served. The dynamic nature and the overall combination of For example, Fig. 51 shows a study of a real gem upon the all these effects is known as the life of the gemstone. face-up position and ±15-deg tilt position and Fig. 52 shows the same study for the corresponding perfect virtual model. Our ray-tracing methodology is discussed in Appen- dix C. 13 Conclusions This paper develops a methodology for evaluating bril- 12 Summary of Illumination Effects liance, fire, and scintillation in gemstones. The study is Our study is based on the actual observation of several devoted to the round brilliant cut and the concepts and tools effects that depend on the illumination conditions and on developed can be also applied to evaluate fancy cuts. We how structured illumination is produced. When a well-cut have highlighted the illumination effects of brilliance, con- gemstone is observed and no or little light is redirected to trast and dynamic contrast, fire, fire and flash scintillation, the observer, the gemstone appears unilluminated. As broad virtual facets, facet interplay, and leakage. The concept of and diffuse illumination is redirected to the observer’s eyes, geometrical angular spectrum has been introduced to under- the stone becomes illuminated and contrast patterns take stand how the cut and the illumination conditions impact a place as shown in Figs. 11 and 13. In the presence of lo- gem’s appearance. We have developed ASET maps, fire calized sources of white light that subtend several degrees, maps, scintillation maps, and glare maps. These maps con- say 3 to 12 deg, several facets across the crown become vey information about the illumination attributes of interest. distinctly brighter. Some facets may appear lightly colored. The ASET maps show the ray directions that can make a In the presence of localized sources of white light that sub- gem to appear illuminated, that is, brilliant. In addition, tend an angle of 1 deg or less, some facets appear colored they show how the obscuration of light by the observer’s with intense colors of the visible spectrum. Facets that re- head plays an important role in creating structured illumi- direct light from localized bright sources appear as light nation. We emphasize that creating structured lighting is

Fig. 48 Comparison of ASET photograph of a real gem ͑a͒ and the computer-generated ASET image ͑b͒.

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Fig. 50 Photographs of a round brilliant showing light dispersion as a function of the size of the clipping aperture. Camera f stops: ͑a͒ f/10, ͑b͒ f/20, ͑c͒ f/30, ͑d͒ f/40, and ͑e͒ the corresponding fire map is also shown for reference.

crucial in producing illumination appeal in gemstones. We The map matrices that are presented show upon face-up have found out that the angular spectrum of the round bril- position how the illumination properties vary as a function liant cut is rich enough that, in movement, the probability of crown and pavilion angles. We have noted that the cut- of aiming at a given light source is high. Therefore and for ter’s trade-off extends not only to brilliance properties but comparison purposes, the phenomenon of fire is mainly de- also to fire and scintillation properties. In particular, we pendent on the light dispersion produced by a gem. Thus, introduced the anti-cutter’s line where stone properties sig- the fire maps that we have introduced show the potential of nificantly change and the cutter’s lines where properties are a given gem to exhibit fire. The scintillation maps presented kept substantially the same. The main cutter’s line contains show the intrinsic light scrambling properties of a given cut the stones with best illumination properties. As a result of and simulate the appearance of a stone as it is observed. noting the cutter’s trade-off, the problem of finding the best The light scrambling contributes to the creation of struc- stones is simplified by one dimension in the cut space. tured lighting and in turn to the creation of scintillation. We We have introduced tilt views along the anti-cutter’s line have divided scintillation into fire and flash scintillation. and along the main cutter’s lines that permit one to find out

Fig. 52 Tilt study of the correspondent perfect virtual gemstone at Fig. 51 Tilt study of a real gemstone at −15, 0, and +15 deg. −15, 0, and +15 deg.

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Fig. 53 Tilt view of the angular spectrum upon the primary refrac- tion along the main cutter’s line. ͑High-resolution image available online only. ͓URL: http://dx.doi.org/10.1117/1.2769018.19͔͒

Fig. 56 Tilt view ASET maps with 40 deg of obscuration and upon the primary refraction along the anti-cutter’s line. ͑High-resolution Fig. 54 Tilt view of the angular spectrum upon the primary refrac- image available online only. tion along the anti-cutter’s line. ͑High-resolution image available on- ͓URL: http://dx.doi.org/10.1117/1.2769018.22͔͒ line only. ͓URL: http://dx.doi.org/10.1117/1.2769018.20͔͒

Fig. 55 Tilt view ASET maps with 40 deg of obscuration and upon the primary refraction along the main cutter’s line. ͑High-resolution Fig. 57 Tilt view, dynamic contrast along the main cutter’s line. image available online only. ͑High-resolution image available online only. ͓URL: ͓URL: http://dx.doi.org/10.1117/1.2769018.21͔͒ http://dx.doi.org/10.1117/1.2769018.23͔͒

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Fig. 59 Contrast around the hemisphere upon the face-up position and along the main cutter’s line. ͑High-resolution image available online only. ͓URL: http://dx.doi.org/10.1117/1.2769018.25͔͒

education tool in the jewelry industry. With the body of knowledge presented in this paper a gem appraiser can readily and substantially evaluate the gem attributes of bril- liance, fire, and scintillation.

Fig. 58 Tilt view, dynamic contrast along the anti-cutter’s line. Appendix A: Tilt Views along the Main Cutter’s ͑ ͓ High-resolution image available online only. URL: Line and Anti-cutter’s Line http://dx.doi.org/10.1117/1.2769018.24͔͒ For completeness Figs. 53–60 provide additional angular spectrum maps and tilt views. which is the most brilliant, the most dispersive, and the Appendix B: Gem Specifications most scintillating stone. These tilt views clearly show the Tolkowsky cut as a compromise between contrast-brilliance Tables 1 and 2 show the specifications for a high- properties and fire properties. performance princess and emerald cut. The maps have been generated by tracing rays in virtual Appendix C: Ray Tracing gems. Quantitative data can be extracted directly from ray tracing to form metrics for gem qualitative evaluation. We Analysis of gemstones involves nonsequential ray tracing have defined some metrics in terms of percentages of ray in which an algorithm searches for the next facet to inter- directions per crown zone, in terms of average dispersion sect after a given ray has encountered a facet. The order in per crown zone, and in terms of virtual facet distribution by which a ray intersects facets is not specified in advance but crown zone. The value of these metrics as it refers to their determined as the ray proceeds. This search after each ray ability to measure realistic illumination attributes is a sub- intersection significantly slows down the ray-tracing pro- ject of continued study. In addition, how the metrics are cess. Ray-tracing speed is a critical issue to render infor- used for the purposes of gemstone grading is important and mation nearly instantaneously, for real-time animations and will be the subject of a future paper. We also have developed the ASET instrument, which produces actual angular spectrum maps. These maps have a strong correlation with computer-generated maps. Of prac- tical importance is the ray-tracing methodology that we have developed for generating the maps. Essentially, ray- tracing speed has been accelerated and the maps can be generated in a fraction of a second even though nonsequen- tial ray tracing is involved for tracing the typically 40,000 rays needed for each map. The methodology and concepts that we have developed can also be applied for evaluating fancy cuts provided that the reduction in angular spectrum is accounted by further subdivision of the illuminating hemisphere. Overall, we have developed understanding in the main mechanics by which gems exhibit the illumination at- tributes of brilliance, fire, and scintillation. We also have Fig. 60 Contrast around the hemisphere upon the face-up position introduced a variety of maps that are valuable for assessing and along the anti-cutter’s line. ͑High-resolution image available on- gem illumination performance. These maps are a valuable line only. ͓URL: http://dx.doi.org/10.1117/1.2769018.26͔͒

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Fig. 61 High-performance princess cut and its constructional parameters.

Fig. 62 High-performance emerald cut and its constructional parameters.

Fig. 64 Very large, very fine forward fire map matrix. ͑High- Fig. 63 Very large, very fine ASET matrix. ͑High-resolution image resolution image available online only. ͓URL: available online only. ͓URL: http://dx.doi.org/10.1117/1.2769018.27͔͒ http://dx.doi.org/10.1117/1.2769018.28͔͒

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Table 1 Princess Cut ͑see Fig. 61͒. As an example of the use of accelerated ray tracing we present Fig. 63, which is called a very large, very fine ͑ ͒ Upper Lower VLVF dense ASET matrix. The dense matrix contains an Pavilion Pavilion Pavilion Pavilion array of 250 by 250 of individual ASET maps for the par- Table % Crown 1 Crown 2 1 2 Ratioa Ratioa ticular constructional parameters of a princess cut. The gen- eration of a VLVF dense matrix permits one to identify 66% 37.3 34.5 60.3 39.2 65% 12% deg deg deg deg regions in the cut space containing gemstones that are bril- liant. By also creating a VLVF fire-map matrix, as shown in aThe pavilion is cut with three tiers of chevron facets. Fig. 64, and comparing it to the VLVF ASET matrix, one can look for common areas that are brilliant and fiery. The VLVF dense matrices are a valuable searching tool given for searches through the design space. Standard nonsequen- that gemstone cuts have many degrees of design, which tial ray tracing may take tens of seconds to produce a single produce a large number of combinations that greatly grows ASET map, which requires about 40,000 rays to achieve with each design parameter added. proper resolution. This speed is considered slow and im- Ray-tracing at two wavelengths for fire-map creation has proper for real-time animations. One way to speed up the the problem that rays at different wavelengths may intersect image rendering is by the use of polygonal ray tracing different facets rather than following the same sequence of where the vertices of convex regions are identified and then facets. To reduce this problem our Fire Maps were gener- ray traced. This significantly reduces the number of rays ated by tracing rays at wavelengths 519 nm and 521 nm that need to be traced since the interior of the polygons are and then the results were scaled to approximate the disper- painted with a color derived from vertex information. Po- sion at the chosen wavelengths of 420 nm and 620 nm. lygonal ray tracing requires finding out how a beam of light is partitioned into polygons as it enters and propagates through a gemstone. Other issues in ray tracing gemstones are modeling and rendering.33,34 Acknowledgments We have chosen not to perform polygonal ray tracing We would like to thank the American Gem Society and but accelerate our non-sequential ray tracing by using the JCK Magazine for supporting this research and acknowl- concept of path memory. In this concept the path of the edge the expertise that our colleagues have shared with us. next ray to be traced is guessed to be the path of the pre- Gabi Tolkowsky has shared his views about diamond vious ray, which is stored in memory. Then the ray is traced beauty. Sergei Sivovolenko from Octonus and Yuri Shele- in sequential mode with the path already stored in memory. mentiev from the Moscow State University have shared If this guess is incorrect then the ray-tracing engine as- their many years of experience in understanding illumina- sumes a nonsequential mode. By doing the ray tracing in a tion effects in gemstones. Martin Haske from the Adamas spiral curve, starting at the center of the gem table, it is Gemological Laboratory has provided useful suggestions possible to produce an ASET map in less than 1 s. The and has been a valuable critic of our methodology. Gary spiral curve passes by every pixel that needs to be painted Holloway has raised many useful issues about diamond cut- with a color that depends on the information obtained by ting that have impacted our views. Bruce Harding, who first the ray trace. determined that an observer affects the appearance of a A second improvement in speed results from the obser- gemstone, has provided significant help in the area of gem- vation that the virtual facets of a gemstone are geometri- stone cutting. Michael Cowing from ACA Gem Laboratory cally convex regions. That the virtual facets are convex is has brought to our attention the importance of contrast and explained by the fact that the intersection of convex regions brightness in creating brilliance in gemstones. We thank Al is also convex. That is, when a beam of light enters a gem- Gilbertson from the Gemological Institute of America and stone it is partitioned into convex regions since the facets Richard von Sternberg from EightStar Diamond Company are convex. The partitioned convex beam remains convex for sharing their pioneering work about the color coding of as it is further partitioned by convex regions. Therefore, angular ranges in gemstone evaluation. The published pa- rather than ray tracing pixel by pixel in a spiral curve, we pers from researchers at the Gemological Institute of trace the vertex pixels in a spiral with a width of a few America provided clues and insights into gemstone appear- pixels that is divided into triangles. After proper checks, ance. The work on gemstone fire of Anton Vasiliev, from groups of pixels can be colored according to information LAL Co. in Moscow, has been very helpful. Special ac- derived from the vertices. This bears some similarity to knowledgements are given to all diamond cutters because polygonal ray tracing except that there is no need to deter- their insightful work in creating gemstone beauty is usually mine how the beam is partitioned into polygons. not recognized.

Table 2 Square emerald ͑see Fig. 62͒.

Corner Crown Crown Crown Pavilion Pavilion Pavilion Table % Ratio 1 2 3 1 2 3

47.6% 22.9% 46.9 40.0 34.0 47.6 39.2 31.2 deg deg deg deg deg deg

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References Gemological Center, Department of Geology, Main Building, Mos- cow State University, Leninskie Gory, GSP-2, Moscow, Russia, 1. M. Tolkowsky, Diamond Design: A Study of the Reflection and Re- 119992. fraction of Light in a Diamond, Spon & Chamberlain, New York 27. Y. Kawabuchi and T. Matsumura, “Cut design of diamond for orna- ͑1919͒, ͗http://www.folds.net/diamond_design/index.html͘. mental use,” U.S. Patent No. 6,694,778 ͑2004͒. 2. T. Shigetomi and K. Inoue, “Device for judging brilliancy of precious 28. P. Yantzer, “The effects of indexed upper half facets,” ͗http:// stones as diamonds or the like,” U.S. Patent No. 4,647,194 ͑1987͒;a journal.pricescope.com/Articles/15/1/The-Effects-of-Indexed-Upper- description of the FireScope® is given by R. Von Sternberg, “Today’s Half-Facets.aspx͘. Revolution in Diamond Cutting,” ͑2002͒, ͗http://www.eightstar.com/ 29. T. Blodgett, A. Gilbertson, R. Geurts, B. Green, M. Johnson, I. Rein- images/Eightstar_Diamond.pdf͘. itz, and P. Yantzer, “Painting and digging out: variations on standard 3. A. Gilbertson, “Device for judging symmetry, brightness, and effi- brillianteering of round brilliant diamonds,” Rapaport Diamond Rep. ciency of light return in precious stones,” U.S. Patent No. 6,795,171 28͑21͒, 239–245 ͑2005͒. ͑2004͒; see also, A. Gilbertson Letting Light Speak for Iitself: An 30. P. Slegers, Infinity Diamonds, Private Communication ͑2005͒. Introduction to Diamond Cut Grading, Diamond Profile, Inc., Port- 31. K. Girdharal, Inc., India, Private Communication ͑2006͒. land, Oreg. ͑1998͒. 32. M. Haske, “Fire demonstration tool and method for using thereof,” 4. J. Sasian, P. Yantzer, and T. Tivol, “The optical design of gemstones,” U.S. Patent Application 2005/0254037 A1. Opt. Photonics News 14͑4͒, 24–29 ͑Apr. 2003͒. 33. S. W. Thomas, “Dispersive refraction in ray tracing,” Visual Comput. 5. A. B. Meinel and E. S. Meinel, “Investigation of the optical behavior 2͑1͒,3–8͑Jan. 1986͒. of brilliant cut diamonds,” report to Helio Associates, Tucson, Ari- 34. Y. Yuan, T. L. Kunii, N. Inamoto, and L. Sun, “Gemstone fire: adap- zona ͑1974͒. ͑ ͒ ͑ ͒ ͑ tive dispersive ray tracing of polyhedrons,” Visual Comput. 4 5 , 6. B. Harding, “Faceting limits,” Gems. Gemol. 15 3 78–88 Fall 259–270 ͑Sep. 1998͒. 1975͒, ͗http://lgdl.gia.edu/pdfs/gemsandgemology/freebackissues/ fall_1975.pdf͘. 7. B. Harding, “Diamond design revisited,” ͗http://www.gemology.ru/ cut/english/tolkow2͘. Jose Sasian is a professor at the University of Arizona, Optical 8. J. S. Dodson, “A statistical assessment of brilliance and fire for the Sciences College. His professional interests are in optical design, round brilliant cut diamond,” Opt. Acta 25͑8͒, 681–692 ͑1978͒, teaching optical sciences, optical fabrication, alignment and testing, ͗http://www.gemology.ru/cut/english/dodson1.htm͘. telescope technology, opto-mechanics, light in gemstones, lithogra- 9. GemCad software, Gemsoft Enterprises, ͗http://www.gemcad.com͘. phy, illumination optics, and light propagation. 10. DiamCalc software, Octonus Co., ͗http://www.octonus.com/oct/ products/3dcalc/standard͘. 11. ASAP, Breault Research Organization, ͗http://www.breault.com͘. 12. FRED, Photon Engineering, ͗http://www.photonengr.com͘. Jason Quick received his BS degree in mathematics from MIT in 13. LightTools, Optical Research Associates, ͗http:// 1995. He worked at MIT’s Laboratory for Computer Science where www.opticalres.com͘. he studied cellular automata and developed algorithms related to 14. TracePro, Lambda Research, ͗http://www.lambdares.com͘. image processing and 3D graphics. Mr. Quick currently is with the 15. ZEMAX, ZEMAX Development Corp., ͗http://www.zemax.com͘. R&D department at the American Gem Society Laboratories. His 16. T. S. Hemphill, I. M. Reinitz, M. L. Johnson, and J. E. Shigley, professional interests include computer modeling, optics, algorithm “Modeling the appearance of the round brilliant cut diamond: an analysis of brilliance,” Gems. Gemol. 34͑3͒, 158–183 ͑Fall 1998͒, design, spectroscopy, and gemstone analysis. ͗http://www.gia.edu/gemsandgemology/18578/1945/563 /back_issue_article_detail.cfm͘. 17. I. M. Reinitz, M. L. Johnson, T. S. Hemphill, A. M. Gilbertson, R. H. Jacob Sheffield received his BA in film from UNLV in 2004. He has Geurts, B. D. Green, and J. E. Shigley, “Modeling the appearance of been with the American Gem Society Laboratories since 1999 and the round brilliant cut diamond: an analysis of fire, and more about has worked in the R&D department since 2004. Mr. Sheffield’s pro- ͑ ͒ ͑ ͒ ͗ brilliance,” Gems. Gemol. 37 3 , 174–197 Fall 2001 , http:// fessional interests at the laboratory include systems analysis, com- www.gia.edu/gemsandgemology/18578/447/64/ back_issue_article- _detail.cfm͘. puter modeling, graphic arts, and spectroscopy. In his spare time, he 18. S. Sivovolenko, Y. Shelementiev, and A. Vasiliev, “The results of pursues his interests in electronic music composition, film, and other diamond cut studies carried out in Moscow State University,” ͑1999͒, multimedia art forms. ͗http://www.cutstudy.com/cut/english/document4.htm͘. 19. S. Sivovolenko, Y. Shelementiev, V. Onischuk, and G. Holloway, “On the problem of grading the quality of diamond cut: an analysis of Jim Caudill is the Director of Advanced Instruments for the Ameri- ͑ ͒ ͗ some aspects of the problem,” 2002 , http://www.gemology.ru/cut/ can Gem Society. Prior to his current position, he worked as an english/grading1/index.htm͘. 20. M. Cowing, “Diamond brilliance: theories, measurements and judg- analyst in the microprocessor industry for 10 years and then as a ment,” J. Gemmol. 27͑4͒, 209–227 ͑Oct. 2000͒. researcher at AGS laboratories from 2000 to 2004. Mr. Caudill’s 21. M. Cowing, “Describing diamond beauty—assessing the optical per- professional interests include engineering, scientific instrumenta- formance of a diamond,” J. Gemmol. 29͑5/6͒, 274–280 ͑2005͒. tion, optics, photo microscopy, lecturing, and gemstone analysis. In 22. S. Sivovolenko, Y. Shelementiev, G. Holloway, J. Mistry, and S. 2007, he received certification in the LEAN Aerospace Initiative at Oulin, Eds., Proc. First Intl. Diamond Cut Conf., Moscow, Russia, MIT. Mr. Caudill is a professional musician/writer/producer and has April 23–26, 2004, Russian Gemological Society, Gemological Cen- performed throughout the US for over 20 years. ter, Department of Geology, Main Building, Moscow State Univer- sity, Leninskie Gory, GSP-2, Moscow, Russia, 119992. 23. Sarin, Sarin Technologies Ltd., ͗http://www.sarin.com/ webviewer.asp͘. Peter Yantzer is the Executive Director at the American Gem Soci- 24. Helium, Octonus Co., ͗http://www.octonus.ru/oct/products/helium/ ety Laboratory. Mr. Yantzer graduated in 1972 as a gemologist and polish͘. was with the Gemological Institute of America from 1972 to 1979 25. A. Vasiliev, “Rainbow in a colorless gem,” Acta Universitatis Wrat- where he served as a staff gemologist, instructor, and laboratory islaviensis, No. 1607, Prace geologiczno-mineralogiczne XLIV, p. director. He has been with the American Gem Society Laboratory 147 ͑1995͒, ͗http://www.gemology.ru/cut/english/rainbow͘. 26. S. Sivovolenko and Y. Shelementiev, “Different model of illumina- since 1995. His professional interests are in the jewelry industry, in tion,” in Proc. First Intl. Diamond Cut Conf., S. Sivovolenko, Y. gemstone cut technology, and gemstone grading. Mr. Yantzer re- Shelementiev, G. Holloway, J. Mistry, and S. Oulin, Eds., p. 48, ceived the American Gem Society’s Robert M. Shipley Award in Moscow, Russia, April 23–26, 2004, Russian Gemological Society, 2005.

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